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C: Physical Processes in Nanomaterials and Nanostructures

Atomic and Electronic Structure of Two-Dimensional Inorganic Halide Perovskites A MX (N = 1 – 6, a = Cs, M = Pb and Sn, and X = Cl, Br, and I) From Ab Initio Calculations n+1

n

3n+1

Anu Bala, Arpan Krishna Deb, and Vijay Kumar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11322 • Publication Date (Web): 15 Mar 2018 Downloaded from http://pubs.acs.org on March 15, 2018

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The Journal of Physical Chemistry

Atomic and Electronic Structure of Two-dimensional Inorganic Halide Perovskites An+1MnX3n+1 (n = 1 – 6, A = Cs, M = Pb and Sn, and X = Cl, Br, and I) from Ab initio Calculations Anu Bala,*,a Arpan Krishna Deb,a,b and Vijay Kumara,c a

Center for Informatics, School of Natural Sciences, Shiv Nadar University, NH-91, Tehsil

Dadri, Gautam Buddha Nagar 201314, Uttar Pradesh, India #b

Step by Step School, Plot No. A-10, Sector 132, Taj Expressway, Noida 201333, Uttar

Pradesh, India c

Dr. Vijay Kumar Foundation, 1969, Sector 4, Gurgaon 122001, Haryana, India

ABSTRACT: Thin layers of inorganic halide perovskites An+1MnX3n+1 (n = 1 – 6, A= Cs, M = Pb and Sn, and X = Cl, Br, and I) have been studied in orthorhombic and cubic phases along with layers of monoclinic CsSnCl3. It is found that one unit-cell-thick layers have low stability except monoclinic phase of CsSnCl3 where formation energy is slighly less than bulk value. However Cs2PbI4 is unstable in both cubic and orthorhombic phases. The formation energy for n > 3 becomes comparable to bulk but the inclusion of spin-orbit coupling is found to be important for the stabilization particularly for layers with Pb. Importantly, layers of environment friendly Sn based systems have similar values of the formation energy in orthorhombic and cubic phases as well as similar band gaps which make them good materials for solar cell applications as temperture range changes during their opration. The studied 66 cubic and orthorhombic nanosystems have direct band gap (0.6 - 2.9 eV) using generalized gradient approximation for the exchange-correlation functional but the use of HSE06 method increases the band gap. The reduced dimensionality leads to elongation (contraction) of MX6 octahedra perpendicular (parallel) to the plane of the layers and an increase in the band gap. 1 ACS Paragon Plus Environment

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The presence of surface makes the hybridization between M s/p and X p orbitals near the valence band maximum stronger than in bulk which is good for light absorption. The effective mass of the electrons and holes is very light which augers well for the transport properties. Lead based systems have larger band gap and these can be useful in applications such as light emitting diodes.

INTRODUCTION Conversion of solar energy into electricity is one of the key green technologies of the 21st century to reduce world reliance on fossil fuels for energy generation and to keep environment clean. In order to achieve this, reduction in cost, higher conversion efficiencies, and long life time of devices are the crucial factors to make photovoltaic technologies economically viable and competitive for wide commercial use. Recent developments in high efficiency and low cost of solar cells produced from organo-metallic perovskites of the form AMX3 (where A = Cs, CH3NH3, or HC(NH2)2; M = Pb and Sn, and X = Cl, Br, and I)1,2 have attracted great interest worldwide. These cells, much like organic solar cells, can be easily produced, and are inexpensive.2 Currently the efficiency of perovskite solar cells for converting photons into electricity is up to about 22.7%.3 While this progress in methylammonium lead iodide based cells and other related systems is remarkable, there remain major challenges to solve including the presence of toxic lead, hysteresis, and instability under ambient air, irradiation, and heat exposure.4 To deal with toxicity, there are efforts to replace lead with less toxic tin5 and other alkaline earth metals6 in the search of better metal substitutes. The hysteresis loss due to the presence of methylammonium can be controlled by either choosing an inorganic substitute or a non-polar organic entity. It has been shown that Cs-based devices are as efficient as, and more stable than those based on methylammonium, after aging for two weeks.7 2 ACS Paragon Plus Environment

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Recently

synthesis

of

very

thin

layers

of

hybrid

perovskites

(CH3(CH2)3NH3)2(CH3NH3)n−1PbnX3n+1(X=Br and I) 8-11 ( up to n = 5) has been reported and it has inspired their use as low-cost semiconductors in optoelectronics.9,12-14 Experimentally a wide range of controllable processing methods are available to prepare thin films, for example by solution-phase growth method,11 spin coating,15 layer-by-layer deposition,16 and intercalation of large organic molecules.17 One unit-cell-thick layers of (C6H9C2H4NH3)2PbI4 (n = 1) have been produced by micromechanical exfoliation18 method and these have shown promising electronic and optical properties. In these hybrid layered systems CH3NH3 occupies the A cation sites as in bulk AMX3 while CH3(CH2)3NH3, the larger molecule, occupies the A sites on the surfaces of the layers. Thus layered perovskites can be formed by incorporating a variety of large organic cations which occupy A sites on the surfaces of the layers and eliminate the restriction on the size of the organic cation by Goldschmidt’s rule. In contrast to their 3D counterparts AMX3, such thin layers of perovskites show enhanced chemical stability against moisture due to the linking of large size organic molecules such as CH3(CH2)3NH3 on the surface.9,12,19 From the point of view of massive production, it is also desirable to make solar cells as thin as possible to save material. Therefore, atomically thin perovskite layers have emerged as a new class of materials with unique properties that are potentially important for electronic and photonic technologies.20 Also, quantum confinement of charge carriers in 2D could show novel properties by changing the thickness of the layers and this makes the study of such systems very interesting as the properties can be tuned to suit an application. Therefore, these layered structures afford greater tunability, which may provide additional routes for material optimization. In the present work, we consider layers of inorganic CsMX3 perovskites with M = Pb and Sn, and X = Cl, Br, and I. We investigate the atomic structure and electronic properties by varying the thickness of the layers in the search of finding systems with good stability,

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non-toxicity, and required band gap. In such layers the stoichiometry is slightly different from the bulk and it can be written as An+1MnX3n+1 with n, an integer representing the thickness of the layers in terms of the unit cell of the perovskite. These systems provide a bridge between 2D and 3D systems21 and offer the possibility to study the effects of dimensionality. For simplicity and for understanding the 2D quantum confinement effects we do not consider organic molecules on the surfaces and limit ourselves to fully inorganic layers. In an earlier theoretical study, Yakobson and coworkers22 have reported structural stabilities, electronic, optical, and transport properties of one unit-cell-thick layers of A2MX4 where A = Cs, Rb, and CH3NH3. In general, 2D semiconducting materials have larger band gap compared to the corresponding bulk and it approaches the bulk value as the thickness of the layer is increased.23 Also the spatial confinement in a 2D structure leads to strongly bound excitons with low mobility.24 Such tightly bound excitons are difficult to dissociate into free carriers at room temperature and the localized charge carriers are unlikely to reach the electron/hole selective contacts in a typical solar cell geometry. This problem can be reduced or omitted by considering an intermediate structure that can approach bulk structure properties. Therefore, we study layered structures having thickness of one to six unit cells in order to understand the variation in properties with thickness. Zhang and Liang have also studied layers of Cs2PbI4 with tetragonal structure.25 Their results reveal that the band gap and exciton-binding energy vary linearly with 1/n for n ≥ 3. However, note that there are phase transitions in the structure of the perovskites with temperture. At low temperatures these perovskites favor orthorhombic structure and around or above room temperature a cubic phase becomes favorable. Therefore, in the present work, we focus on both the cubic and orthorhombic phases in order to check the variation in properties with phase change. The cubic phase is interesting from the point of view of applications considering the temperature of operation of the solar cells. In the case of CsSnCl3, monoclinic phase is preferred below


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379K. Therefore, in this case we have studied the bulk as well as layers in monoclinic structure instead of orthorhombic phase. Also, we have considered one unit-cell-thick layers with n = 1 in tetragonal structure as it is a stable phase in the intermediate temperature range in bulk. Recently there have been studies26, 27 on thin layers of A2MX4 (M = Sn, Pb and X= Br, I) and BPbI4 perovskites with different types of mono or divalent organic cations on the surfaces. These studies showed the effect of interlayer distance and octahedron distortion on the band gap and electronic properties. Additionally, it has been found that most defects in layers of these perovskites are either inactive28 or only introduce shallow or no states in the band gap.29 This can be helpful to have good transport and optical properties. Therefore, the present study can serve as a guideline to choose an appropriate material from the pool of 2D inorganic perovskites for dfferent photovoltaic applications.

COMPUTATIONAL METHOD The calculations have been carried out using projector augmented wave (PAW) pseudopotential method as implemented in Vienna Ab initio Simulation Package (VASP).30 For exchange-correlation functional, we use the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE).31 Further, we have studied the effects of spin-orbit coupling (SO) on the formation energy of the structures and the band gap. In general, within GGA, the calculated band gap is underestimated compared with the experimental value. Nevertheless, in these perovskite systems it has been reported that GGA without including SO effects reproduces the experimental band gap well32 but the band gap is underestimated when SO coupling is included. This can be understood in terms of the cancellation of errors due to (i) the underestimation of the band gap by PBE functional and (ii) the overestimation of the band gap when SO coupling is excluded.33 The band structures obtained from 5 ACS Paragon Plus Environment


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improved methods such as GW approximation34,35 and hybrid functional36 are essentially similar to those deduced from PBE calculations.37 Also earlier calculations on tin and lead halide perovskites suggest that calculations within PBE and without SO coupling neither change the orbital character of the band-edge states nor the k-point at which the band gap occurs.37 Therefore, to reduce the cost of heavy computation for more than 69 nanoscale systems and bulk, we have calculated the band gap using PBE. It is hoped that our results would give a reasonable estimate of the band gap value and the trends. This is further strengthened by the very recent calculations on layers of CsPbI3 and MAPbI3, where the value of the band gap calculated within PBE and PBE0+SO lies in a close range.25 We have calculated the band gaps with PBE+SO in some cases to show the effect of SO. We first studied bulk CsMX3 (M = Sn and Pb; X = Cl, Br, and I) perovskites in cubic, tetragonal, and orthorhombic phases. All of them undergo structural distortions and phase transitions as the temperature is varied. At low temperatures these compounds have orthorhombic structure while at intermediate temperatures they acquire tetragonal structure except for CsSnCl3 which transforms from monoclinic to cubic phase.38 At sufficiently high temperatures (often at or near room temperature), all of these compounds are known to adopt undistorted cubic (Fm3m) perovskite struture39 in which M atom is at the center of the cubic unit cell surrounded by the octahedron of halogen atoms that occupy the face centers. The alkali atoms occupy the corners as shown in Figure 1. As the temperature is lowered, distortions lead to tetragonal (with rotation of octahedron in the plane) and/or orthorhombic structures (with octahedron rotation in and out of plane (Figure 1)). We have studied all the three phases in bulk as well as in one unit-cell-thick layers, but for thicker layers only cubic and orthorhombic cases are considered as the tetragonal structure tends to adopt a similar structure as obtained from the cubic phase. The orthorhombic phase of CsSnCl3 is not considered because it prefers monoclinic structure below 379K. The layers of perovskites


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have been obtained by slicing the corresponding bulk along (001) crystallographic plane as shown in Figure 1 for the orthorhombic and cubic phases and inset of Figure 2 for the monoclinic phase. The

Figure 1: (a) Part of the orthorhombic AMX3 bulk perovskite from which An+1MnX3n+1 layers are formed. A supercell of one unit-cell-thick layer is also shown. (b) A unit cell of cubic bulk and unit cells for layers of different thickness with n = 1 – 6. Cs, halogen (Cl, Br, and I), and Pb/Sn atoms are shown by green, purple, and grey (slightly visible inside the octahedra) balls, respectively.

stoichiometry of layers in orthorhombic and cubic structures is different from bulk but the layers in monoclinic structure have the bulk stoichiometry because the monoclinic structure itself has a layered structure (Figure 2). The structural optimization and total energy calculation of the layers (bulk) are performed using 15x15x1 (15x15x15 for cubic and 11x11x5 for orthorhombic phases) k-points mesh. For the monoclinic structure of CsSnCl3 we used 15x11x2 k-points for bulk and 15x11x1 k-points for the layers. The plane wave cut7 ACS Paragon Plus Environment


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off energy to expand the wave function is taken to be 500 eV in all the cases. The unit cell dimensions as well as the ionic positions have been relaxed until the absolute value of the force on each ion becomes less than 1 meV/Å. The study of the orthorhombic and tetragonal structures has been done with a unit cell having two metal halide octahedra in order to explore any distortion that may arise due to the orientation change of the octahedra.

RESULTS AND DISCUSSIONS We optimized the atomic structures of the layers and calculated the formation energy, Ef = Etot(An+1MnX3n+1) – (n+1)E(AX) – nE(MX2) of orthorhombic and cubic phases while for monoclinic structure, the formation energy is calculated from Ef = Etot(AnMnX3n) – nE(AX) – nE(MX2), in order to study their stability against decomposition into binary halides AX and MX2. Here Etot is the total energy of the layers or bulk perovskite, and E(Y) is the total energy of the bulk binary halide Y. The latter is given in Table S1 in Supporting Information. A negative value of Ef corresponds to stable layers or bulk system. First we discuss the monoclinic phase of bulk CsSnCl3 (shown in Figure 2) which is structurally differrent from the other studied compounds. The monoclinic phase is formed with highly distorted edge sharing octahedra while its cubic phase has corner sharing octahedra. The calculated bulk lattice parametrs: a = 15.91 Å, b = 5.705 Å, c = 7.411 Å, and γ = 92.85° (angle between a and b lattice vectors) are in better agreement with experimental values40 (a = 16.10 Å, b = 5.748 Å, c = 7.425 Å, and γ = 93.2°) than the LDA results41 which underestimate the lattice contants (a = 15.37 Å, b = 5.529 Å, c = 7.132 Å, and γ = 93.12°). The band gap calculated with GGA (2.57 eV) exchange-correlation functional from this work is slightly lower than the LDA value41 (2.74 eV), and both types of exchange-correlation functionals underestimate the gap as compared to the experimental value40 (4.5 eV). The 8 ACS Paragon Plus Environment

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layers of monoclinic CsSnCl3 with the same stochiometry as bulk are nearly as stable as bulk as shown in Figure 2. This stability can be contributed to the fact that the bulk is formed of these weakly interacting layers as one can see from the structure shown in Figure 2. The band gap in layers increases by ~ 0.5 eV (Figure 2) as compared to 2.57 eV in bulk. This GGA value of the band gap shows that these layered materials are less suitable for solar cells due to their large band gap.

Figure 2: The formation energy and band gap of CsSnCl3 bulk and layers in monoclinic structure. The corresponding unit cells are shown in inset. Atoms Cs, halogen (Cl, Br, and I), and Sn are shown by blue, green, and grey (slightly visible inside the half octahedra) colors, respectively.

Next, we considered all the three bulk phases of perovskites which are stable at different temperatures i.e. orthorhombic, tetragonal, and cubic along with their one unit-cellthick layers to check the Ef and therefore the stability of the layers as compared to the corresponding bulk. The values of Ef of these systems are given in Table S2 in Supplementary Information and partly also in Table 1.



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As expected, the bulk orthorhombic structure has the highest absolute value of Ef and this agrees with the fact that it is the most stable structure at low temperatures while the cubic structure is least favourable and the tetragonal bulk structure has an intermediate value of Ef. Further, Sn based bulk halide perovskites are more stable than Pb based bulk perovskites except for bromides in the orthorhombic phase which have similar values. CsPbI3 is the least stable among all the studied bulk materials. Experimentally also, the fabrication of this perovskite material needs much care for making a device and it is formed only inside vacuum as a slight energy change can decompose this system into its consititutents.42

Table 1: Formation energy (eV/atom) without and with SO coupling (values in parenthesis) using PBE exchange-correlation functional for perovskite layers in cubic and orthorhombic (in bold) phases. Here ‘n’ represents the thickness of the layers in terms of the number of unit cells.

Csn+1PbnCl3n+1 Csn+1PbnBr3n+1 Csn+1PbnI3n+1 Csn+1SnnCl3n+1 Csn+1SnnBr3n+1 Csn+1SnnI3n+1

a

n=1 -0.003(-0.007) -0.019(-0.022) (-0.018a) -0.004(-0.006) -0.019(-0.020) (-0.006a) 0.033 (0.031) 0.016 (0.015) (0.037a) -0.022(-0.023) -0.072* -0.014(-0.015) -0.015(-0.015) (-0.019a) ~0 (-0.001) -0.007(-0.008) (-0.004a)

n=2 -0.035(-0.040) -0.047(-0.050)

n=3 -0.046(-0.050) -0.056(-0.060)

n=4 -0.051(-0.055) -0.062(-0.065)

n=5 -0.053(-0.058) -0.065(-0.068)

n=6 -0.055(-0.059) -0.067(-0.070)

Bulk -0.065(-0.068) -0.079(-0.082)

-0.036(-0.038) -0.047(-0.048)

-0.045(-0.048) -0.056(-0.058)

-0.048(-0.052) -0.061(-0.063)

-0.051(-0.055) -0.064(-0.066)

-0.053(-0.056) -0.066(-0.068)

-0.060(-0.063) -0.077(-0.079)

0.008 (0.005) -0.005(-0.007)

0.002(-0.002) -0.011(-0.014)

0.0004(-.004) -0.014(-0.017)

-0.001(-0.005) -0.016(-0.019)

-0.001(-0.006) -0.018(-0.021)

-0.004(-0.006) -0.025(-0.028)

-0.055(-0.056) -0.081* -0.046(-0.046) -0.048(-0.048)

-0.061(-0.065) -0.083* -0.055(-0.056) -0.056(-0.056)

-0.070(-0.071)

-0.073(-0.073)

-0.075(-0.075)

-0.060(-0.060) -0.061(-0.061)

-0.062(-0.062) -0.063(-0.064)

-0.064(-0.064) -0.065(-0.065)

-0.083(-0.084) -0.087* -0.070(-0.072) -0.075(-0.075)

-0.029(-0.030) -0.030(-0.031)

-0.037(-0.037) -0.038(-0.038)

-0.041(-0.041) -0.042(-0.042)

-0.042(-0.042) -0.044(-0.045)

-0.044(-0.044) -0.046(-0.046)

-0.046(-0.046) -0.056(-0.056)

Values with PBE+SO for the orthorhombic one unit-cell-thick layers are from Ref. [22]

*Monoclinic phase values For 2D systems, in general the trend of Ef is the same as seen for the bulk counterparts but the magnitude of Ef decreases as shown in Figure 3. Also, the orthorhombic phase 10 ACS Paragon Plus Environment

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remains the most stable phase in 2D systems and the cubic phase has the least stability. In the case of CsSnCl3, the Ef in the monoclinic phase is -0.087 eV/atom compared with the value of -0.083 eV/atom for the cubic phase. For other Sn based systems, interestingly both the cubic and orthorhombic layers have very nearly the same values of the Ef (see Table 1). This implies that the stability of layers of Sn based inorganic perovskites is not much affected with the increase in temperature. The stability of both of these phases decreases in going from Cl to Br to I. Also, Sn based systems are more stable compared with those of Pb except for bromides as in the case



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Figure 3. Comparison of the formation energy for the layers of different inorganic perovskites with the respective bulk value. In the case of Csn+1SnnCl3n+1 the values are given only for the cubic phase as it occurs in monoclinic phase below 379 K (see Figure 2).

of bulk for which the values are similar. Further, we find that the difference in Ef between bulk cubic and tetragonal phases is more than between orthorhombic and tetragonal phases. Therefore, the transition of tetragonal phase to orthorhombic phase is more favorable in the case of bulk, but this trend changes in 2D systems specially for n = 1 layers of Cs2SnX4 where cubic and tetragonal phases have equal Ef (Table S2 in Supporting Information). Our results show that the inclusion of SO interaction in the calculation of the ground state energy is very important especially for Pb as it lowers the Ef of Pb(Sn) based perovskites up to 0.05 (0.004) eV/formula unit. Our results for the orthorhombic one unitcell-thick layers are in line with those previously reported22 (see Table 1). The slight difference in the magnitude of Ef can be attributed to very dense (15x15x1) k-points mesh and larger vacuum space (more than 15Å) used in our calculations. These high values are chosen to check the reliability of our results for one unit-cell-thick layers as the values of Ef are small. It is interesting that the one unit-cell-thick layers of inorganic perovskites are stable except for Cs2PbI4 (in all the three phases) as it can be seen from Table S1 in Supporting Information. Our results show that among the corner sharing octahedra geometries, one unitcell-thick layers of Cs2SnCl4 in the cubic phase (stable at high temperature) and Cs2PbCl4 in the orthorhombic phase (stable at low temperatures) with Ef values of -0.023 eV/atom and 0.022 eV/atom, respectively, are the most stable among all n = 1 layers we have studied (see Table 1). Interestingly, the most stable n = 1 system is the monoclininc CsSnCl3 layer (Ef = 0.072 eV/atom) with egde sharing octrahedra structure. 12 ACS Paragon Plus Environment

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Experimentally also, very thin films of tin halide perovskites fabricated by utilizing phenylethylammonium (PEA) as an organic separating interlayer have been shown significant enhancement in stabilty in air atmosphere compared to their three-dimensional counterparts.43 Recent calculations also reveal that removing phenylethylammonium iodine from 2D perovskite network requires more energy than methylammonium iodine from its bulk counterpart.44 As the number of layers in the cubic and orthorhombic phases increases, the results (Table 1 and Figure 3) show that the stability of layers increases and for n > 3, Ef achieves 75-80% of the bulk value except for Csn+1PbnI3n+1. In the latter case SO interactions are important to stabilize the cubic phase with n = 3 and 4 as it can be seen from Table 1. For layers with n = 5, Ef achieves about 80% of the bulk value in the orthorhombic and cubic phases. It is seen from Figure 3 that the energy difference between the orthorhombic and cubic phases is very small for Csn+1SnnX3n+1 layers compared with Csn+1PbnX3n+1 layers. In general the stability is higher for Sn layers and it can be enhanced if I is replaced by Br and further by Cl. Therefore, all the studied inorganic systems with about five unit-cell-thick layers can give stability comparable to bulk. Further, enhancement in the stabilty is possible by protecting the surface of 2D sheets by organic molecules45 as some long-chain organic cations afford a degree of hydrophobicity, and superior moisture stability.46 The atomic structure analysis of the layers shows that the layers of cubic bulk become non-symmetric after optimization due to elongation of MX6 octahedra along the z-direction (perpendicular to the plane of the layers). At the same time the bonds in MX6 octahedra in the plane of the layers become shorter than in bulk and this increases the strength of the M-X bonds in the plane of the layer. This can be seen from the bond length values given in Table S2 in Supporting Information. On increasing the thickness of the layer, the MX6 octahedra in the central layer tend to achieve the bulk behavior as the bond lengths become comparable to 13 ACS Paragon Plus Environment


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the value in bulk, while the surface MX6 octahedra are still affected by the surface effects and the Cs atoms relax inwards of the surface layer (the Cs-Cs distance between two consecutive atoms in the z-direction decreases in one unit-cell-thick layer compared with the bulk value and then it gradually increases with n). The maximum effect is obtained for the case of iodides. A similar behavior of the stretching of the octahedra along the z-axis is obtained for the orthorhombic structure. We also find that the change of M-X-M bond angle in the layer is very significant compared to the bulk, and therefore the octahedra in the one unit-cell-thick layers are distorted. This finding is similar to the organic perovskite layers.47 The reduced MX bond length in the layer suggests increased interatomic interactions for n = 1 systems. But, for thicker layers, there is increase in the M-X bond lengths in the layer which tend to achieve the bulk value in the plane. Interestingly, all the layers of different thicknesses are direct band gap semiconductors (see Table 2, and Figures 4 and 5) as also the bulk. Our calculated band gap for bulk cubic phase is in agreement with previous PBE value39 and it is about 0.5 eV lower than the HSE06 value (Table 2) which also agrees with the earlier results.48 We have also performed HSE06 calculations for layers of Csn+1SnnI3n+1 with n = 1-3 in order to check the behavior in layers and the resulting band structure is similar to the one obtained by using PBE, the primary change being widening of the band gap (Table 2) as unoccupied conduction band states shift to higher energies. The reduction in the dimensionality increases the band gap49,50 and our calculated values are on an average ~0.4 eV and ~0.6 eV larger for the one unit-cell-thick layers of Csn+1PbnX3n+1 and Csn+1SnnX3n+1, respectively, compared with the bulk value. The band gap gradually approaches the bulk value with the increase in the layer thickness as shown in Figure 5 where a linear curve is fitted to the values for n ≥ 2. The band gap values for n = 1 show strong quantum confinement due to which it does not fit to the linear curve and these effects slowly get dimished with increasing thickness of the layers. 14 ACS Paragon Plus Environment

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The quantum confinement effects offer tunability of the band gap with varying thickness as it has

been

also

found

experimentally

for

semiconducting

layers

of

(CH3(CH2)3NH3)2(CH3NH3)n-1PbnI3n-1 (n = 1, 2, 3, and 4) perovskites.9 The phase transition

from orthorhombic to cubic phase decreases the band gap on an average by ~0.3 eV for the layers of Csn+1PbnX3n+1 for all the values of n and X. This value slightly decreases when Pb cation is replaced with Sn2+ (see Table 2). Semiconductors with a direct band gap in the range of 1.0 eV to 1.5 eV are highly desirable as this corresponds to near-infrared spectral range that is important for solar energy harvesting. Commercially used silicon (indirect band gap = 1.17 eV) and CdTe (direct band gap of about 1.5 eV) have desirable band gaps. Our calculations show (Figures 4 and 5) that few layers of Csn+1SnnX3n+1 (X = Cl and Br) and Csn+1PbnI3n+1 have the band gap of ~1 eV within GGA and therefore, these systems can be promising candidates for photovoltaic applications. On the other hand Csn+1PbnX3n+1 (X = Cl and Br) layers have the band gap value of about 2 eV and these systems can be used in light emitting diodes for violet (2.76 eV), blue (2.51 eV) and green (2.2 eV) colors.51, 52 The values calculated with PBE+SO for the cubic and orthorhombic phases (Table 2) show that SO interactions decrease the band gap by ~ 0.8 eV for Csn+1PbnX3n+1 layers and ~ 0.2 eV for Csn+1SnnX3n+1 layers.



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Figure 4. Band gap for cubic and orthorhombic phases of inorganic perovskite layers. Unfilled (filled) bars and symbols represent the calculated band gap values with PBE (PBE+SO) for the cubic and orthorhombic phases, respectively. For Csn+1SnnCl3n+1 results are given only for the cubic phase.


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Figure 5. Band gap for cubic and orthorhombic bulk and layers (n = 1-6) without spin-orbit interactions. For Csn+1SnnCl3n+1 results are given only for the cubic phase. We have fitted the points (except for n = 1) with a line to show the behavior as 1/n changes.



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Table 2: The calculated values of the direct band gap (eV) for different perovskite layers in cubic and orthorhombic phases using PBE and PBE+SO (values in parenthesis). Results for the orthorhombic phase are given in bold. n represents the number of unit-cell-thick layers as shown in Figure 1. The band gap for the cubic phase occurs at the symmetry point M (0.5, 0.5, 0.0) and for the orthorhombic case at the symmetry point Γ. Tc represents the transition temperature at or above which the cubic phase exists. n=1 2.62(1.78) 2.92(2.26) (2.80)a

n=2 2.48(1.58) 2.78(1.94)

n=3 2.40(1.45) 2.69(1.79)

n=4 2.35(1.35) 2.65(1.70)

n=5 2.32(1.29) 2.62(1.65)

n=6 2.29(1.23) 2.60(1.61)

Csn+1PbnBr3n+1 Tc = 403 K

2.18(1.39) 2.52(1.90) (2.29a)

2.06(1.21) 2.35(1.56)

1.98(1.07) 2.26(1.42)

1.94(0.98) 2.21(1.33)

1.89(0.90) 2.18(1.27)

1.86(0.84) 2.16(1.23)

Csn+1PbnI3n+1 Tc = 602 K

1.83(1.04) 2.18(1.52) (1.84a)

1.76(0.90) 2.03(1.23)

1.69(0.78) 1.95(1.10)

1.64(0.68) 1.90(1.01)

1.61(0.61) 1.87(0.96)

1.58(0.55) 1.85(0.92)

Csn+1SnnCl3n+1 Tc = 379 K

1.56(1.35)

1.37(1.16)

1.31(1.08)

1.19(0.95)

1.13(0.89)

1.08(0.83)

Csn+1SnnBr3n+1 Tc = 292 K

1.20(0.99) 1.28(1.15) (1.74a)

1.04(0.82) 1.18(1.02)

0.92(0.70) 1.14(0.92)

0.85(0.62) 1.06(0.87)

0.79(0.55) 1.04(0.84)

0.75(0.50) 1.02(0.80)

Csn+1SnnI3n+1 Tc = 425 K

0.97(0.72) 1.44e 1.12(0.92) (1.38a)

0.85(0.60) 1.35e 1.01(0.77)

0.75(0.49) 1.25e 0.96(0.71)

0.69(0.42) 0.93(0.68)

0.64(0.36) 0.90(0.66)

0.60(0.31) 0.86(0.62)

Csn+1PbnCl3n+1 Tc = 320 K

Bulk 2.18 (1.01) 2.21c 2.54 (1.47) 2.92b (1.83)b 3.00d 1.76 (0.60) 1.79c 2.11 (1.08) 2.41b(1.32)b 2.23d 1.46 (0.23) 1.49c 1.82 (0.78) 2.00b(0.86)b 0.97 (0.62) 1.01c 1.52b(1.19)b 0.61 (0.25) 0.65c 0.93 (0.62) 1.14b(0.80)b 0.44 (0.03) 0.48c 0.81 (0.47) 0.87b(0.49)b

a

HSE06+SO values for one unit cell thick layer in the orthorhombic phase from Ref. [22] HSE06+SO values for the bulk cubic phase from Ref. [48] c PBE values for the bulk cubic phase from Ref. [39] d Experimental values for bulk from Ref. [53] e Present work with HSE06 b

The site projected density of states for bromides has been shown in Figure 6(a) as representative of these systems. One can see that the valence band maximum (VBM) is formed of Br p states and Pb/Sn s states whereas the conduction band minimum (CBM) is mainly composed of Pb/Sn p states and some of the Br p states. There is an increase in the Br

p states near the VBM in surface and subsurface layers compared with bulk. The semi-core 18 ACS Paragon Plus Environment

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electronic p levels from Cs (only shown for n = 6 in Figure S2 in Supporting Information) are located deep in the VB while the density of states from s levels lies in the CB. The cation (Cs+) indirectly affects the M-X interactions by contracting or expanding the lattice according to the size. Bader charge analysis shows that the value of the electronic charge on Sn is 12.96 e and on Pb it is 12.88 e in bulk perovskites as compared to 14 e treated as valence charge in their atomic state. Nearly the same values of Bader charge have been obtained on M atom in layers. This suggests some covalent bonding between Sn and X while it is mainly ionic between Cs and X with Cs acting as charge donor in bulk as well as in layers. There is increased hybridization between Sn/Pb s states and p states of X ions in the surface layers near the top of the VB compared with bulk as it can be seen from the charge density plot in Figure 6(b) from the states in the vicinity of the VBM. Also layers of Csn+1SnnX3n+1 have lower band gap than Csn+1PbnX3n+1 layers. This behavior is similar to bulk. It is due to fact that Sn 5s states lie higher in energy in comparison to Pb 6s states and closer to X p states. This makes Sn s-X p bonding stronger than Pb s- X p bonding in the VBM region. As VBM is an anti-bonding state of M s and X p, the stronger coupling between Sn s and X p upshifts the VBM and decreases the band gap. On changing the halogen from Cl to Br to I, the band gap generally decreases for bulk as well as layered systems. This is due to the fact that VBM contains X p character and the energy levels of the p states of X shift upwards from Cl to Br to I which upshift the VBM edge resulting in a decrease in the band gap. Therefore, we see that the type of interactions remains similar in low dimensions of these inorganic perovskites.



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Figure 6: (a) Site projected density of states per atom with angular momentum decomposition in the cubic phase of Csn+1SnnBr3n+1 (n = 1 and 2) and Csn+1PbnBr3n+1 (n = 1 and 2) along with the bulk. (b) Projected charge density near VBM with isosurface value 0.003 e/Å3.


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The band structure plots are shown in Figures 7 and 8. For the bulk cases these are in agreement with previous results and the band gap is obtained at the same symmetry points of cubic and orthorhombic phases.54,55 The curvature of the bands in the vicinity of VBM and CBM in the orthorhombic structure is similar whereas in the cubic phase the CB is shallower than the VB. Inclusion of SO coupling leads to shifting of the bands near the CBM to lower energy as it is shown for Csn+1PbnI3n+1 layers in inset of Figure 8. A similar behavior has been obtained for bulk as well. The effect of SO interactions is more on Pb systems as compared to Sn systems, and it can be seen in particular near the CBM of these inorganic perovskites (bulk and layers). The bands in the range of -4 eV to -2 eV arise dominantly from the p orbitals of halogens (Cl, Br, and I). The larger contribution of Sn and Pb s (l = 0) states to the VBM and Sn/Pb p (l = 1) states to the CBM suggests that stronger optical transitions may occur between the VBM and CBM (delta l = 1) and hence our results suggest that the presence of surfaces in layered systems of perovskites may enhance absorption in solar cell applications.



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Figure 7: Band structure plots for bulk CsSnI3 and CsSnBr3 in orthorhombic phase and their layers with 1 to 3 unit cell thickness. The VBM is taken as reference of energy. The value of the band gap is given in each case.


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Figure 8: Band structure plots for the cubic phase of bulk CsSnI3 and CsPbI3 and their layers. The effect of inclusion of spin-orbit interactions on bands in the vicinity of the VBM and CBM is shown in inset. The change in the band structure can be seen particularly near the CBM. The VBM is taken as reference for energy (dash line). The band gap occurs at the symmetry point R (0.5, 0.5, 0.5) of bulk and M (0.5, 0.5, 0.0) of a unit cell thick layer.

In Table 3, we have given the effective masses obtained by fitting the energy bands with parabolic curves at VBM and CBM in the orthorhombic phase. In general the electrons and holes are light and Sn based systems have charge carriers lighter than Pb based systems in bulk and in layers. Also, the effective masses of holes ∗ ) and electrons (∗ ) change only slightly as the number of layers is changed. However we can get additional advantage from 23 ACS Paragon Plus Environment


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layered structure in which the flatter band near the CBM is absent in comparison to bulk (Figure 7). Therefore, layers in orthorhombic phase are expected to have good transport properties also.

Table 3. Effective masses (in units of me) of electrons and holes for the orthorhombic layers ∗ ∗ at the CBM (∗ ) and VBM (∗ ) without spin-orbit coupling. corresponds to

effective mass of electrons in flatter (stepper) band close to CBM (Figure 7) of CsMX3. n=1 ∗ ∗ )

n=2 ∗ ∗ )

n=3 ∗ ∗ )

n=4 ∗ ∗ )

Csn+1PbnCl3n+1

0.235 (0.281)

0.228 (0.231)

0.222 (0.225)

0.219 (0.207)

0.734, 0.212 (0.192)

Csn+1PbnBr3n+1

0.210 (0.265)

0.208 (0.203)

0.198 (0.205)

0.187 (0.195)

0.726, 0.175 (0.168)

Csn+1PbnI3n+1

0.168 (0.321)

0.125 (0.215)

0.127 (0.210)

0.132 (0.212)

0.809, 0.104 (0.173)

Csn+1SnnBr3n+1

0.132 (0.092)

0.130 (0.091)

0.127 (0.088)

0.121 (0.081)

0.680, 0.110 (0.070)

Csn+1SnnI3n+1

0.112 (0.087)

0.098 (0.079)

0.084 (0.074)

0.087 (0.070)

0.620, 0.090 (0.067)

System

Bulk ∗ ∗ , ∗ )

Our results on these inorganic perovskite layers show that environmental friendly Csn+1SnnX3n+1 (n > 3, X = Br and I) systems have almost degenerate stable cubic and orthorhombic phases with band gap ~1eV. Therefore, we can think of better phase stability of solar cells which may operate over wide temperature range with these layers as absorber material. The additional feature of strong hybridization between s orbital of Sn and p orbitals of X also make them attractive. Also the effective mass in these systems is quite small and therefore we expect good electron and hole transport. On the other hand, Pb based layers have larger band gaps and these can also be useful in optoelctronics devices.


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CONCLUSIONS In summary, we have studied layers of inorganic halide perovskites in different phases that are stable in different temperature ranges i.e. cubic (room/high) and orthorhombic/monoclinic (low) in search of lead free and stable systems for photovoltaic applications. Our results show that the orthorhombic/monoclinic structures are lower in energy than cubic structures but the latter are interesting near the room temperature as these perovskites generally undergo phase transition from orthorhombic/monoclinic phase at low temperatures to cubic phase near room temperature or above. We find that in layers of Sn halides the energy difference between cubic and orthorhombic structures is very small and also there is only a small change in the band gap of about 0.25 eV. Further, in all cases the band gap is direct as also in bulk and the thickness can be used to tailor the band gap for photovoltaic and optoelectronics applications. We find that stable lead-free layers of Csn+1SnnX3n+1 with n ~ 5 already achieve close to bulk properties but still surface effects exist which help to increase the hybridization between the s orbitals of Sn and the p orbitals of X. This is good for having efficient absorbers. Also the band gap for few layer Sn based halides is ~1 eV and the charge carriers are light. These properties make them promising for photovoltaic applications. On the other hand Csn+1PbnX3n+1 layers have higher band gap in the region of 1.6-2.6 eV and these can also be used for light emitting diode applications. The orthorhombic layers show additional feature of light hole in comparison to bulk for good transport properties. ASSOCIATED CONTENT *SSupporting Information The following Supporting Information is available free of charge on the ACS Publications website.



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1) Table S1 which contains the cohesive energy of binary halides. 2) Table S2 which gives the formation energy in eV per formula unit for bulk and layers of CsMX3,

3) Figure S1 which shows different atoms in cubic phase of the considered systems 4) Table S3 which gives variation in bond lengths (Å) in different layers 5) Figure S2 which shows the projected density of states per atom in the cubic phase of Csn+1SnnBr3n+1 for n = 6

AUTHOR INFORMATION Corresponding author *E-mail: [email protected], [email protected] #

Present address

ACKNOWLEDGEMENTS A.B. acknowledges financial support from the Department of Science and Technology (DST), Government of India, through the Project Grant no. SR/WOS-A/PM-1042/2015. The calculations have been performed using the High Performance Computing facility MAGUS of Shiv Nadar University.

REFERENCES 1 2 3 4 5

Yang S.; Fu W.; Zhang Z.; Chen H.; Li C.-Z. Recent advances in perovskite solar cells: efficiency, stability and lead-free perovskite. J. Mater. Chem. A 2017, 5, 11462–11482. Burschka J.; Pellet N.; Moon S.-J.; Humphry-Baker R.; Gao P.; Nazeeruddin M. K.; Grätzel M. Sequential deposition as a route to high-performance perovskitesensitized solar cells. Nature 2013, 499, 316-319. https://www.nrel.gov/pv/assets/images/efficiency-chart.png Version 10-30-2017. Grätzel M. The light and shade of perovskite solar cells. Nature Materials 2014, 13, 838-842. Hao F.; Stoumpos C. C.; Cao D. H.; Chang R. P. H.; Kanatzidis M. G. Lead-free solid-state organic–inorganic halide perovskite solar cells. Nat. Photonics 2014, 8, 489-494.


Page 27 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6

7 8 9 10

11 12

13 14

15

16 17 18 19 20

Pazoki M.; Jacobsson T. J.; Hagfeldt A.; G. Boschloo G.; Edvinsson T. Effect of metal cation replacement on the electronic structure of metalorganic halide perovskites: replacement of lead with alkaline-earth metals. Phys. Rev. B 2016, 93, 144105(1)- 144105(10). Kulbak M.; Gupta S.; Kedem N.; Levine I.; Bendikov T.; Hodes G.; Cahen D. Cesium enhances long-term stability of lead bromide perovskite-based solar cells. J. Phys. Chem. Lett. 2016, 7(1), 167–172. Stoumpos C. C.; Cao D. H.; Clark D. J.; Young J.; Rondinelli J. M.; Jang J. I.; Hupp J. T.; Kanatzidis M. G. Ruddlesden–popper hybrid lead iodide perovskite 2D homologous semiconductors. Chem. Mater. 2016, 28, 2852–2867. Cao D. H.; Stoumpos C. C.; Farha O. K.; Hupp J. T.; Kanatzidis M. G. 2D homologous perovskites as light-absorbing materials for solar cell applications. J. Am. Chem. Soc. 2015, 137, 7843–7850. Stoumpos C. C.; Soe C. M. M.; Tsai H.; Nie W.; Blancon J.-C.; Cao D. H.; Liu F.; Traoré B.; Katan C.; Even J. et. al. High members of the 2D Ruddlesden-Popper halide perovskites: synthesis, optical properties, and solar cells of (CH3(CH2)3NH3)2(CH3NH3)4Pb5I16. Chem. 2017, 2, 427-440. Dou L.; Wong A. B.; Yu Y.; Lai M.; Kornienko N.; Eaton S. W.; Fu A.; Bischak C. G.; Ma J.; Ding T. et. al. Atomically thin two-dimensional organic-inorganic hybrid perovskites. Science 2015, 349, 1518-1521. Tsai H.; Nie W.; Blancon J.-C.; Stoumpos C. C.; Asadpour R.; Boris H.; Neukirch A. J.; Verduzco R.; Crochet J. J.; Tretiak S. et. al. High-efficiency two-dimensional Ruddlesden–Popper perovskite solar cells. Nature 2016, 536, 312–316. Yuan M.; Quan L. N.; Comin R.; Walters G.; Sabatini R.; Voznyy O.; Hoogland S.; Zhao Y.; Beauregard E. M.; Kanjanaboos P. et al. Perovskite energy funnels for efficient light-emitting diodes. Nat. Nanotechnol. 2016, 11, 872-877. Blancon J. C.; Tsai H.; Nie W.; Stoumpos C. C.; Pedesseau L.; Katan C.; Kepenekian M.; Soe C. M.; Appavoo K.; Sfeir M. Y. et. al. Extremely efficient internal exciton dissociation through edge states in layered 2D perovskites. Science 2017, 355, 1288-1292. Prakash G. V.; Pradeesh K.; Ratnani R.; Saraswat K.; Light M. E.; Baumberg J. J. Structural and optical studies of local disorder sensitivity in natural organic– inorganic self-assembled semiconductors. J. Phys. D: Appl. Phys. 2009, 42, 185405(1)-185405(7). Matsui T.; Yamaguchi A.; Takeoka Y.; Rikukawa M.; Sanui K. Fabrication of twodimensional layered perovskite [NH3(CH2)12NH3]PbX4 thin films using a selfassembly method. Chem. Commun. 2002, 0, 1094-1095. Era M.; Maeda K.; Tsutsui T. Self-organization approach to organic/inorganic quantum-well based on metal halide-based layer perovskite. Thin Solid Films 1998, 331, 285-290. Niu W.; Eiden A.; Prakash G. V.; Baumberg J. J. Exfoliation of self-assembled 2D organic-inorganic perovskite semiconductors. Appl. Phys. Lett., 2014, 104, 171111(1)-171111(4). Smith I. C.; Hoke E. T.; Solis-Ibarra D.; McGehee M. D.; Karunadasa H. I. A layered hybrid perovskite solar-cell absorber with enhanced moisture stability. Angew. Chem. Int. Ed. 2014, 53, 11232-11235. Zhang Y.; Liu J.; Wang Z.; Xue Y.; Ou Q.; Polavarapu L.; Zheng J.; Qi X.; Q. Bao. Synthesis, properties, and optical applications of low-dimensional perovskites. Chem. Commun. 2016, 52, 13637-13655. 27 ACS Paragon Plus Environment


21 22 23 24 25 26 27

Page 28 of 30

Mitzi D. B. Synthesis, crystal structure, and optical and thermal properties of (C4H9NH3)2MI4 (M = Ge, Sn, Pb). Chem. Mater. 1996, 8(3), 791-800. Yang J.-H.; Yuan Q.; Yakobson B. I. Chemical trends of electronic properties of two-dimensional halide perovskites and their potential applications for electronics and optoelectronics. J. Phys. Chem. C 2016, 120, 24682-24687. Ishihara T. Optical properties of PbI-based perovskite structures. J. Lumin. 1994, 60-61, 269-274. Muljarov E. A.; Tikhodeev S. G.; Gippius N. A.; Ishihara T. Excitons in selforganized semiconductor/insulator superlattices: PbI-based perovskite compounds. Phys. Rev. B 1995, 51, 14370-14378. Zhang L.; Liang W. Z. How the structures and properties of two-dimensional layered perovskites MAPbI3 and CsPbI3 vary with the number of layers. J. Phys. Chem. Lett. 2017, 8 (7), 1517–1523. Fraccarollo A.; Cantatore V.; Boschetto G.; Marchese L.; Cossi M. Ab initio modeling of 2D layered organohalide lead perovskites. J. Chem. Phys. 2016, 144, 164701(1)-164701(13). Fraccarollo A.; Canti L.; Marchese L.; Cossi M. First principles study of 2D layered organohalide tin perovskites. The Journal of Chemical Physics 2017, 146, 234703(1)-234703(2).

28

Liu Y.; Xiao H.; Goddard III W. A. Two-dimensional halide perovskites: tuning electronic activities of defects. Nano Lett. 2016, 16, 3335-3340.

29

Pandey M.; Jacobsen K. W.; Thygesen K. S. Band gap tuning and defect tolerance of atomically thin two-dimensional organic-inorganic halide perovskites. J. Phys. Chem.Lett. 2016, 7, 4346-4352. Kresse G.; Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169-11186. Perdew J. P.; Burke K.; Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865-3868. Shirayama M.; Kadowaki H.; Miyadera T.; Sugita T.; Tamakoshi M.; Kato M.; Fujiseki T.; Murata D.; Hara S.; Murakami T. N. et. al. Optical transitions in hybrid perovskite solar cells: Ellipsometry, density functional theory, and quantum efficiency analyses for CH3NH3PbI3. Phys. Rev. Appl. 2016, 5, 014012(1) - 014012(25). Even J.; Pedesseau L.; Jancu J.-M.; Katan C. Importance of spin–orbit coupling in hybrid organic/inorganic perovskites for photovoltaic applications. J. Phys. Chem. Lett. 2013, 4(17), 2999-3005. Brivio F.; Butler K. T.; Walsh A.; Schilfgaarde van M. Relativistic quasiparticle self-consistent electronic structure of hybrid halide perovskite photovoltaic absorbers. Phys. Rev. B 2014, 89, 155204(1) - 155204(6). Umari P.; Mosconi E.; Angelis De F. Relativistic GW calculations on CH3NH3PbI3 and CH3NH3SnI3 perovskites for solar cell applications. Sci. Reports 2014, 4, 4467(1) - 4467(7). Menéndez-Proupin E.; Palacios P.; Wahnón P.; Conesa J. C. Self-consistent relativistic band structure of the CH3NH3PbI3 perovskite. Phys. Rev. B 2014, 90, 045207(1) - 045207(7). Yin W.-J.; Yang J.-H.; Kang J.; Yan Y.; Wei S.-H. Halide perovskite materials for solar cells: a theoretical review. J. Mater. Chem. A 2015, 3, 8926-8942. Kuok M. H. Raman study of the phase transition in CsSnCl3. Journal of Raman Spectroscopy 1992, 23, 225-227.

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Grote C.; Ehrlich B.; Berger R. F. Tuning the near-gap electronic structure of tinhalide and lead-halide perovskites via changes in atomic layering. Phys. Rev. B 2014, 90, 205202(1) - 205202(7). Poulsen F. R.; Rasmussen S. E. Crystal structure and phase transition of cesium trichlorostannate (II). Acta Chem. Scand. 1979, 24, 150-156. Huang yi L.; Lambrecht R.L. Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl3, CsSnBr3 and CsSnI3. Phys. Rev. B 2013, 88, 165203(1)-165203-12. Eperon G. E.; Paternò G. M.; Sutton R. J.; Zampetti A.; Haghighirad A. A.; Cacialli F.; Snaith H. J. Inorganic caesium lead iodide perovskite solar cells. J. Mater. Chem. A 2015, 3, 19688-19695. Liao Y.; Liu H.; Zhou W.; Yang D.; Shang Y.; Shi Z.; Li B.; Jiang X.; Zhang L.; Quan L. N. et. al. Highly oriented low-dimensional tin halide perovskites with enhanced stability and photovoltaic performance. J. Am. Chem. Soc. 2017, 139 (19), 6693–6699. Quan L. N.; Yuan M.; Comin R.; Voznyy O.; Beauregard E. M.; Hoogland S.; Buin A.; Kirmani A. R.; Zhao K.; Amassian A. et. al. Ligand-stabilized reduced-dimensionality perovskites. J. Am. Chem. Soc. 2016, 138, 2649−2655. Mitzi D. B. Synthesis, structure, and properties of organic–inorganic perovskites and related materials. Prog. Inorg. Chem. 2007, 48, 1–121. Smith I. C.; Hoke E. T.; Solis-Ibarra D.; McGehee M. D.; Karunadasa H. I. A layered hybrid perovskite solar-cell absorber with enhanced moisture stability. Angew. Chem. Int. Ed. 2014, 126, 11414–11417. Dohner E.R.; Jaffe A.; Bradshaw L. R.; Karunadasa H. I. Intrinsic white-light emission from layered hybrid perovskites. J. Am. Chem. Soc. 2014, 136, 1315413157. Lang L.; Yang J.-H.; Liu H.-R.; Xiang H. J.; Gong X.G. First-principles study on the electronic and optical properties of cubic ABX3 halide perovskites. Phys. Lett. A 2014, 378, 290-293. Sichert J. A.; Tong Y.; Mutz N.; Vollmer M.; Fischer S.; Milowska K. Z.; Cortadella R. G.; Nickel B.; Cardenas-Daw C.; Stolarczyk J. K. et. al. Quantum size effect in organometal halide perovskite nanoplatelets. Nano Letters 2015, 15, 6521-6527. Tyagi P.; Arveson S.M.; Tisdale W.A. Colloidal organohalide perovskite nanoplatelets exhibiting quantum confinement. Phys. Chem. Lett. 2015, 6, 19111917. Kim Y. H.; Cho H.; Heo J. H.; Kim T. S.; Myoung N.; Lee C. L.; Im S. H.; Lee T. W. Multicolored organic/inorganic hybrid perovskite light-emitting diodes. Adv. Mater. 2015, 27, 1248-1254. Tan Z. K.; Moghaddam R. S.; Lai M. L.; Docampo P.; Higler R.; Deschler F.; Price M.; Sadhanala A.; Pazos L. M.; Credgington D. et. al. Bright lightemitting diodes based on organometal halide perovskite. Nature. Nanotechnol. 2014, 9, 687-692. Hao F.; Stoumpos C. C.; Chang R. P. H.; Kanatzidis M. G. Anomalous band gap behavior in mixed Sn and Pb perovskites enables broadening of absorption spectrum in solar cells. J. Am. Chem. Soc. 2014,136, 8094-8099. Jishi R. A.; Ta O. B.; Sharif A. A. Modeling of lead halide perovskites for photovolatic applications. J. Phys. Chem. C 2014, 118, 28344 - 28349,



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Huang yi L.; Lambrecht W. R.L. Electronic band structure, phonons, and exciton binding energies of halide perovskites CsSnCl3, CsSnBr3, and CsSnI3. Phys. Rev. B 2013, 88, 165203 (1-12).

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